This is a Phase I/II, two part trial of recombinant interleukin-2 in symptomatic human immunodeficiency virus-infected children designed to evaluate the safety and maximum tolerated dose of rIL-2, and the effect of various doses of rIL-2 on CD4 cell counts and on viral load. Part A is a dose Phase I/II dose escalating trial. Four patients in each of three dose levels will be enrolled. Twelve to 18 patients will be enrolled in this part of the study. If two of four subjects in any dose level experience >= Grade 3 toxicity, the dose level immediately below that dose level will be declared the maximum tolerated dose (MTD). Part B will provide additional data on the safety of rIL-2 when given at the MTD using these data, it will be possible to calculate tighter confidence limits for the true incidence of toxicity. Also, it will be possible to determine whether administration of rIL-2 has an effect on antigen-induced lymphocyte proliferation and on cytotoxic T and NK cell responses or an effect on the expression of HLA-DR and IL-2 receptor expression on CD4 and CD8 cells.